{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7JZQQHKSOEIXWW5CM7Q4Z7QYFF","short_pith_number":"pith:7JZQQHKS","canonical_record":{"source":{"id":"2402.11397","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-17T22:40:22Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"7ee94e97b7106066b57b97a32679c5bd1f0641c424fecc2ea202a71c21db3869","abstract_canon_sha256":"43ed85d5c1f646ebb5fb02cb74de7a43e6e9b73960663e6d92c4cd46fab5851d"},"schema_version":"1.0"},"canonical_sha256":"fa73081d5271117b5ba267e1ccfe182958d603c36ee471a85e1199da5fa3b11e","source":{"kind":"arxiv","id":"2402.11397","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.11397","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"arxiv_version","alias_value":"2402.11397v1","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.11397","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"pith_short_12","alias_value":"7JZQQHKSOEIX","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"pith_short_16","alias_value":"7JZQQHKSOEIXWW5C","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"pith_short_8","alias_value":"7JZQQHKS","created_at":"2026-07-05T07:46:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7JZQQHKSOEIXWW5CM7Q4Z7QYFF","target":"record","payload":{"canonical_record":{"source":{"id":"2402.11397","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-17T22:40:22Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"7ee94e97b7106066b57b97a32679c5bd1f0641c424fecc2ea202a71c21db3869","abstract_canon_sha256":"43ed85d5c1f646ebb5fb02cb74de7a43e6e9b73960663e6d92c4cd46fab5851d"},"schema_version":"1.0"},"canonical_sha256":"fa73081d5271117b5ba267e1ccfe182958d603c36ee471a85e1199da5fa3b11e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:46:38.642749Z","signature_b64":"Q2F8XLw4awIjjb2C+EehNg6wjDRcepkgY88P5NEQgkYCxmkAcaA+ZOXWAElLlE92JIAFJAbTaLBs3CykvMr7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa73081d5271117b5ba267e1ccfe182958d603c36ee471a85e1199da5fa3b11e","last_reissued_at":"2026-07-05T07:46:38.642252Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:46:38.642252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.11397","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:46:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QU1DoyH/pIDMxlVIKpyfh4CsUQ6j52ez8SWcDVorPCjMM9vgBVqP99VuYRfJ5oR+oNVhZA7e1quDYK3YGdZhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:31:20.630575Z"},"content_sha256":"ccab7bb33a8f305274e5a6f42801bd3c49c19406010a39c453fe89b82ab71aeb","schema_version":"1.0","event_id":"sha256:ccab7bb33a8f305274e5a6f42801bd3c49c19406010a39c453fe89b82ab71aeb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7JZQQHKSOEIXWW5CM7Q4Z7QYFF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Gianluca Fabiani","submitted_at":"2024-02-17T22:40:22Z","abstract_excerpt":"We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal weights and biases, offering computational efficiency. We demonstrate that there exists a choice of external weights, for any family of such RPNNs, with non-polynomial infinitely differentiable activation functions, that exhibit an exponential convergence rate when approximating any infinitely differentiable function. For illustration purposes, we test the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.11397","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.11397/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:46:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e04hTuPtfPCy6tvrdxj0IgTctZlMn+fZ+JrmSwRbXzJwBQUd+Mrjm+035zJ2bzQqsfkmkoLjnHapFIfbnazvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:31:20.631110Z"},"content_sha256":"41a893fc05b991305de32cd664de1861d318e861fbff396d4fd9d4c00fe9a09e","schema_version":"1.0","event_id":"sha256:41a893fc05b991305de32cd664de1861d318e861fbff396d4fd9d4c00fe9a09e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7JZQQHKSOEIXWW5CM7Q4Z7QYFF/bundle.json","state_url":"https://pith.science/pith/7JZQQHKSOEIXWW5CM7Q4Z7QYFF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7JZQQHKSOEIXWW5CM7Q4Z7QYFF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T07:31:20Z","links":{"resolver":"https://pith.science/pith/7JZQQHKSOEIXWW5CM7Q4Z7QYFF","bundle":"https://pith.science/pith/7JZQQHKSOEIXWW5CM7Q4Z7QYFF/bundle.json","state":"https://pith.science/pith/7JZQQHKSOEIXWW5CM7Q4Z7QYFF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7JZQQHKSOEIXWW5CM7Q4Z7QYFF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7JZQQHKSOEIXWW5CM7Q4Z7QYFF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"43ed85d5c1f646ebb5fb02cb74de7a43e6e9b73960663e6d92c4cd46fab5851d","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-17T22:40:22Z","title_canon_sha256":"7ee94e97b7106066b57b97a32679c5bd1f0641c424fecc2ea202a71c21db3869"},"schema_version":"1.0","source":{"id":"2402.11397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.11397","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"arxiv_version","alias_value":"2402.11397v1","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.11397","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"pith_short_12","alias_value":"7JZQQHKSOEIX","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"pith_short_16","alias_value":"7JZQQHKSOEIXWW5C","created_at":"2026-07-05T07:46:38Z"},{"alias_kind":"pith_short_8","alias_value":"7JZQQHKS","created_at":"2026-07-05T07:46:38Z"}],"graph_snapshots":[{"event_id":"sha256:41a893fc05b991305de32cd664de1861d318e861fbff396d4fd9d4c00fe9a09e","target":"graph","created_at":"2026-07-05T07:46:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.11397/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal weights and biases, offering computational efficiency. We demonstrate that there exists a choice of external weights, for any family of such RPNNs, with non-polynomial infinitely differentiable activation functions, that exhibit an exponential convergence rate when approximating any infinitely differentiable function. For illustration purposes, we test the pro","authors_text":"Gianluca Fabiani","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-17T22:40:22Z","title":"Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.11397","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ccab7bb33a8f305274e5a6f42801bd3c49c19406010a39c453fe89b82ab71aeb","target":"record","created_at":"2026-07-05T07:46:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"43ed85d5c1f646ebb5fb02cb74de7a43e6e9b73960663e6d92c4cd46fab5851d","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-17T22:40:22Z","title_canon_sha256":"7ee94e97b7106066b57b97a32679c5bd1f0641c424fecc2ea202a71c21db3869"},"schema_version":"1.0","source":{"id":"2402.11397","kind":"arxiv","version":1}},"canonical_sha256":"fa73081d5271117b5ba267e1ccfe182958d603c36ee471a85e1199da5fa3b11e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa73081d5271117b5ba267e1ccfe182958d603c36ee471a85e1199da5fa3b11e","first_computed_at":"2026-07-05T07:46:38.642252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:46:38.642252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q2F8XLw4awIjjb2C+EehNg6wjDRcepkgY88P5NEQgkYCxmkAcaA+ZOXWAElLlE92JIAFJAbTaLBs3CykvMr7AA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:46:38.642749Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.11397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccab7bb33a8f305274e5a6f42801bd3c49c19406010a39c453fe89b82ab71aeb","sha256:41a893fc05b991305de32cd664de1861d318e861fbff396d4fd9d4c00fe9a09e"],"state_sha256":"a90203ac76d6b44832185cd660cbc68a5198395913434ed2c189a8775345a893"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/eD1GoAtCb2ys7uyuAofmuax/dtTnbQsyaPJmeelFH85E+qrvL6Y+TXIr2lpm8i5y4GL9eD1buM+9TAwSfpbBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:31:20.634954Z","bundle_sha256":"093f92c987e175fd6619d7524f3a8cc2bacc6634b70cd3263d97f9cbf68c9109"}}